Bacterial spore based energy system

ABSTRACT

A method and system for providing an engine for producing mechanical energy through the absorption and evaporation of moisture uses a hygroscopic material in one or more configurations to do mechanical work. The hygroscopic material can include microbial spores, plant cells and cell materials, silk and hydrogel materials that absorb moisture and expand or swell when exposed to high relative humidity environments and shrink or return to nearly their original size or shape when exposed to low relative humidity environments wherein the moisture evaporates and is released. By exposing the hygroscopic material to a cycle of high relative humidity environments and low relative humidity environments, useful work can be done. One or more transmission elements can be used to couple the hygroscopic material to a generator that converts the mechanical energy to, for example, electrical energy. The hygroscopic material can be applied to flexible sheet materials that flex as the hygroscopic material absorbs or evaporates moisture. The hygroscopic material can also be applied to elastic conductive materials, such that the plates of a capacitor mechanically change the capacitance of the device.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. application Ser.No. 13/998,857 filed Jul. 23, 2013 which is a 35 U.S.C. §371 NationalPhase Entry application of International Application No.PCT/US2011/061869 filed Nov. 22, 2011, which designates the U.S., andwhich claims any and all benefits under 35 U.S.C. §119(e) of U.S.Provisional Application No. 61/415,902 filed Nov. 22, 2010, the contentsof which are incorporated herein by reference in their entireties.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

Not Applicable

REFERENCE TO MICROFICHE APPENDIX

Not Applicable

BACKGROUND

Technical Field of the Invention

The present invention relates to systems that can store and releaseenergy using hygroscopic materials. Specifically, systems based onhygroscopic materials can be selectively exposed to high or low humidityenvironments in order to cause the materials to expand or contract to douseful work as well as store and release energy.

Description of the Prior Art

Natural evaporation across open water facilitates the energy exchangebetween oceans and atmosphere, thereby fueling the winds and warmweather on earth. Under dry atmospheric conditions evaporation can beharnessed to do useful work, for example, the tree uses evaporation totransport water from soil to the leaves. Plants also use swelling andshrinking of cell walls for mechanical actuation. These processes haveinspired novel approaches to engineering actuators, pumps, biologicalsensors and even energy scavengers to power micro- and nano-devices. Inprinciple, evaporation has the potential to become a significant sourceof renewable energy. However, this requires useful work to be generatedfrom evaporation with high efficiency, high power levels, long termsustained performance, and without consuming fresh water.

Bacterial spores are dormant cells that can withstand harshenvironmental conditions for long periods of time and still maintainbiological functionality (FIG. 1a ). Despite their dormancy, spores areremarkably dynamic structures. For example, Bacillus spores respond tochanges in relative humidity (RH) by expanding and shrinkinganisotropically and changing their diameter by as much as 12% (FIG. 1b). The density of fully hydrated and expanded spores are significantlylower than dry spores; ˜1.2 g/ml vs. ˜1.5 g/ml for B. subtilis. Thereduction of mass density despite absorption of additional materialrequires spores to expand their volume highly efficiently.

SUMMARY

The striking durability, dynamic response, and efficient use of waterhave motivated us to investigate their use in energy conversion fromnatural absorption and evaporation. In accordance with the invention,the swelling-shrinking cycle of microbial spores, such as bacterialspores, shows promise for economically feasible generation of renewableenergy from natural evaporation. These and other hygroscopic materials,such as mutant spores, plant cells and plant cell materials, and silkcan be used to store and generate energy.

In accordance with various embodiments of the invention, the hygroscopicmaterial can be coupled to a generator by a transmission to transferenergy generated by the hygroscopic material as it expands and/orcontracts from exposure to moisture and/or humidity. In accordance withsome embodiments of the invention, the hygroscopic material can beadhered to a flexible surface or enclosed in an expandable container. Inthese embodiments, the addition of moisture causes the hygroscopicmaterial to expand resulting in the flexing of the flexible surface in afirst direction or expansion of the container and the removal ofmoisture causes the hygroscopic material to contract resulting in theflexing of the flexible surface in a second direction or contraction ofthe container. The motion and forces generated by the expanding orcontracting hygroscopic material can be converted to electrical energyusing a generator.

In accordance with one embodiment of the invention, the hygroscopicmaterial can be adhered to a flexible sheet material that includes apiezo electric material or is coupled to a piezo electric device, forexample by a transmission. The hygroscopic material can be exposed to aplurality of cycles composed of a low relative humidity environmentfollowed by a high relative humidity environment causing the hygroscopicmaterial to release moisture and shrink and then absorb moisture andexpand. The resulting expansion and contraction caused the piezoelectric material or the piezo electric device to generate electricity.

In accordance with an alternate embodiment of the invention, thehygroscopic material can be used to vary the space and area of adielectric material separating two plates of a capacitor. The plates canbe formed from a flexible conductive material and separated by one ormore layers of hygroscopic material or a dielectric elastomer material.The plates can be biased with a voltage potential and the hygroscopicmaterial can be exposed to a plurality of cycles composed of a lowrelative humidity environment followed by a high relative humidityenvironment causing the hygroscopic material to release moisture andshrink and then absorb moisture and expand. The shrinking and expandingof the hygroscopic material can cause the distance between the platesand/or the area of the plates to change, resulting in a change incapacitance and generating electricity.

In accordance with a further embodiment of the invention, thehygroscopic material can be used in a device that stores energy. Thehygroscopic material can be placed in an enclosed, expandable containerthat is compressed. As long as the hygroscopic material remains sealedaway from moisture, the device will store energy. To release the energy,water or moist air can be introduced into the container causing thehygroscopic material to absorb moisture and expand causing the containerto expand releasing the stored energy. A plurality of energy storagedevices can be combined to enable the generation of larger quantities ofenergy. The energy storage devices can be coupled to an energyconversion device for converting the mechanical energy to electricalenergy.

These and other capabilities of the invention, along with the inventionitself, will be more fully understood after a review of the followingfigures, detailed description, and claims.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1A shows a scanning electron microscope image of B. subtilisspores, the scale bar represents 500 nm.

FIG. 1B shows a diagram of the sporehydration/swelling-dehydration/shrinking cycle, according to theinvention.

FIG. 1C shows a diagram of a system for using spores to generate energyto deform a sheet of flexible material, according to one embodiment ofthe invention.

FIGS. 2a-f show the dynamics of spore expansion and contractionaccording to one embodiment of the invention. FIGS. 2a and 2b showimages of the (2 a) front and (2 b) back sides of a silicon AFMcantilever with spores immobilized on the back side. The RH of the airsurrounding the cantilever was periodically cycled every 5 seconds. FIG.2c shows a graph of the change in surface stress over time and FIG. 2dshows a graph of the relative change in mass over time. FIG. 2e shows agraph of the change in surface stress over time where the cycle periodwas reduced to 2 seconds. FIG. 2f shows a graph of the surface stressafter 1 million cycles at the 2 second period.

FIGS. 3a-e show the application of energy to a flexible materialaccording to one embodiment of the invention. FIGS. 3a-c showphotographs of a rubber sheet at 30%, 60%, and 90% RH. FIG. 3d shows agraph of the radius of curvature (circles) and the plane stress(squares) as function of RH. FIG. 3e shows a graph of free energy asfunction of RH.

FIGS. 4a-e show a system for generating electricity according to oneembodiment of the invention. FIG. 4a shows the curved rubber sheet(beige) fixed to a Lego™ brick (yellow) with adhesive tape (black).FIGS. 4b-c show the rubber sheet placed against a piezoelectrictransducer wherein, when an ultrasonic humidifier provides moisture, thespores swell and the rubber sheet pushes against and deforms thetransducer to generate electricity. FIG. 4d shows the voltage waveformrecorded during three cycles of high and low RH of the system of FIGS.4b-c . FIG. 4e shows the electrical energy delivered to the 10 M ohminput resistance of an oscilloscope probe.

FIG. 5 shows a graph of power density as a function of RH which can beobtained from systems according to the present invention.

FIG. 6 shows a schematic diagram of an elastic substrate coated with alayer of bacterial spores deformed by stress generated by the sporesaccording to one embodiment of the present invention.

FIGS. 7A and 7B show photographs of crack formation in the spore layer.

FIG. 8 shows a photograph of a system for generating electricityaccording to an embodiment of the present invention.

FIG. 9 shows a close-up photograph of the system of FIG. 8 forgenerating electricity according to an embodiment of the presentinvention.

FIG. 10 shows graphs of evaporation rates (10 a), surface temperature(10 b) and power density (10 c) calculated as a function of surface RHfor a system according to the present invention.

FIGS. 11A and 11B show a device for generating energy having a shutterfor controlling the exposure to high and low RH environments accordingto the invention.

FIGS. 11C-11E show systems based on the embodiments of FIGS. 11A-11B forgenerating electrical energy according to the invention.

FIGS. 12A-12D show a device for generating electrical energy usingbacterial spores according to the invention.

FIGS. 13A-13B show a device for storing energy using bacterial sporesaccording to the invention.

FIGS. 14A-14B show a device for generating energy using bacterial sporesaccording to the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention is direct to methods and systems for generatingand storing energy using hygroscopic materials, such as bacterialspores. Hygroscopic material includes microbial spores, such as sporesof spore forming bacteria, preferably non-pathogenic strains from thebacillus genus, such as, Bacillus atrophaeus, B. subtilis, B. cereus, B.megaterium, B. thuringiensis, B. stearothermophil and Gram-positivebacterial spores, plant cells and plant cell materials (including plantwalls), and silk materials. Other Hydroscopic materials can includecell-free extracts from spores, plant tissues, synthetic biomimetichygroscopic gels, hydrogel based materials, such as pHEMA[Poly(2-hydroxyethyl methacrylate)], Polyacrylamide,detergent-containing ‘cytoskeletal stabilization’ buffers, andhyaluronic acid based polymer based materials. In accordance with theinvention, the hygroscopic material such as bacterial spores can bearranged in various configurations and exposed to varying environmentalconditions that enable the spores to absorb or evaporate moisture. Uponabsorbing moisture, the spores expand and upon releasing moisture, thespores contract. As a result, the spores in the various configurationscan be made to generate energy and do work. The spores, can be coupledusing one or more transmission elements to a generator to convert themechanical energy, for example, into electrical energy.

In addition, the hygroscopic materials, after being exposed to water ormoisture, can be exposed to an evaporating environment, such as low RHor heating or low pressure environment that causes moisture to bereleased from the material and causes the material shrink, substantiallyback to its original size when dry. Sources of heat can include naturaland artificial sun light, as well as other natural and artificial heatsources, including hot springs, geothermal heat sources, and heatreleased by power plants and other industrial equipment or vehicles.

In accordance with the invention, the exposure to or application of highrelative humidity environment includes the direct application of afluid, including water, water vapor and high relative humidity gases,including air and the exposure to or application of low relativehumidity environment includes the direct removal of water and watervapor, for example, by lowering the vapor pressure and/or heating andthe application of low relative humidity gases, including air.

In accordance with various embodiments of the invention, the hygroscopicmaterial can be coupled to a transmission that transfers the forces andenergy generated by the expanding and contracting hygroscopic materialto a generator that converts the forces into energy, such as electricalenergy. In some embodiments, the transmission can be a mechanicallinkage of one or more components, including for example, levers and/orgears. In other embodiments, the transmission can include an arm orsheet material that is coupled to the hygroscopic material (using, forexample, an adhesive material) such that it flexes in response to thechanging volume or shape of the hygroscopic material. The arm or sheetcan be connected to or coupled to a generator to produce energy. Thetransmission can be adapted, for example, using levers and/or gears, tochange the speed and/or force of actuation. The transmission can alsoinclude one or more hydraulic or pneumatic elements and can be adaptedto change the speed or force of actuation by varying the cross-sectionalarea of the fluid or gas flow. The generator can, for example, be anelectromagnetic generator which converts mechanical energy to electricalenergy or a solid state device, such as piezo-ceramic transducer whichconverts mechanical energy to electrical energy. In other embodiments,the generator can be a capacitor that changes its capacitance inresponse to the expanding and contracting hygroscopic material thatforms part of the dielectric of the capacitor. Dielectric elastomerbased generators can also be used. In this embodiment, the hygroscopicmaterial can be coupled to the dielectric elastomer so that changes inthe size of the hygroscopic material changes the capacitance across thedielectric elastomer. See, for example, FIG. 11D.

In accordance with one embodiment of the invention, bacterial spores canbe physically adhered to a sheet of elastic material, drying sporescontract anisotropically and reduce their radius (FIG. 1a ), a processthat is reversible on humidification (FIG. 1b ). The induceddifferential strain causes the sheet to curve (FIG. 1c ), generatingmechanical work. FIG. 1A shows a scanning electron microscope image ofB. subtilis spores. The scale bar represents 500 nm. FIG. 1B shows adiagram of the reversible process of humidification and dehumidificationthat causes the spores to swell and then shrink. FIG. 1C shows a diagramof spores densely adhered to an elastic sheet material. Upon drying thespores contract transferring mechanical energy to the sheet causing itto curl. If the spores are initially fixed in placed in the contractedstate, with the application of moisture, the spores expand transferringmechanical energy to the sheet causing it to curl in the oppositedirection.

To demonstrate the dynamics of force generation, waterabsorption/release, and the response of spores to long term cyclicalexpansion and contraction in a system, B. subtilis spores can be placedon the surface of an atomic force microscope (AFM) cantilever, as shownin FIGS. 2a and 2b , and subjected to changes in relative humidity (RH).This system can be used to measure the changes in surface stress fromthe deflection of the cantilever and the mass of the absorbed watervapor from the shifts in the resonance frequency.

In this embodiment, an AFM cantilever chip (Veeco Instruments, HMX-S)was gently placed on a flat piece of silicon wafer while the cantileverstayed in contact with the surface of the wafer. A solution of spores(˜1 mm in diameter) in water was pipetted onto the cantilever under anoptical microscope and allowed to dry. The cantilever surface wasinspected by optical microscopy to ensure that spore coverage of itssurface. The cantilever was placed into the AFM head (Veeco Instruments,Multimode AFM) with the uncoated side of the cantilever facing the laserbeam.

In order to provide a system for rapid switching of relative humidity,an aquarium pump was used to supply two streams of air travellingthrough plastic tubing. One of the streams was saturated with watervapor by passing it through a bubbler. The other stream carriedlaboratory air at approximately 15-20% relative humidity. The open endsof the tubes were placed near the AFM head with air flowing towards thecantilever. A motorized arm was used to block the air from the tubes oneat a time, switching at the frequency of a square wave supplied by asignal generator. The RH levels experienced by the cantilever weredetermined by first recoding the cantilever deflection signals at highand low RH levels in this setup and then by placing the AFM head in acontrolled humidity chamber to find the steady RH levels that give thesame signal values.

Measurement of changes in plane stress and mass of the cantilever weredetermined as follows: The plane stress σ at the surface of an elasticsubstrate with thickness t, Young's modulus E, and Poisson's coefficientν is related to the radius of curvature r according to Stoney's formula:

$\begin{matrix}{\sigma = {\frac{E}{6\left( {1 - v} \right)}\frac{t^{2}}{r}}} & (1)\end{matrix}$

This formula provides a good approximation if the film generating stressis significantly thinner than the substrate so that the bendingstiffness of the film is negligible. While the thickness of the sporelayer is comparable to the cantilever, we assumed that it has anegligible bending stiffness because it is composed of objects withapproximately circular cross sections. A more general treatment ofcurvature can be found in Reyssat, E. & Mahadevan, L. Hygromorphs: frompine cones to biomimetic bilayers. J. R. Soc. Interface 6, 951-957(2009) which is hereby incorporated by reference. The AFM allowsmeasurement of the slope of the cantilever at the location of the laserspot, rather than measurement of the radius of curvature. However, r canbe related to the slope θ if the position of the laser spot relative tothe cantilever base x is known. Assuming a parabolic profile for thecantilever, the radius is: r=x/θ. The changes in the slope near the freeend of the cantilever were measured to be well beyond the detectorlimits (saturation); therefore we placed the laser spot close to thecantilever base. The exact position of the laser spot was estimated bycomparing the ratio of the thermal noise levels at this location and ata location near the free end of the cantilever, using the analyticalexpression for the mode shape of a rectangular cantilever beam.Thickness of the cantilever was determined to be 1.49 um from the springconstant. Young's modulus and Poisson's coefficient were selected to beE˜130 GPa and ν˜0.278 for silicon (100). The effect of the reflectivealuminum coating (40 nm) was neglected and it was assumed the entirecantilever is made of silicon.

The change in cantilever mass was determined by its effect on theresonance frequency, which is described by the equation ω²=k/m. Here ωis the resonance frequency, k is the cantilever spring constant, and mis the total mass of the cantilever. For relatively small changes inmass;

Δm/m=2Δω/ω  (2)

To make rapid measurements of the shifts in the resonance frequency, thecantilever was driven at a constant frequency near the resonance andthen monitored the phase of oscillations. Phase is related to theresonance frequency according to the formula

$\begin{matrix}{\phi = {\tan^{- 1}\frac{\omega_{d}{\omega/Q}}{\omega_{d}^{2} - \omega^{2}}}} & (3)\end{matrix}$

Here ω_(d) is the drive frequency and Q is the quality factor of theresonance. For the cantilever used for the measurements, ω_(d) waschosen as 12.15 KHz and Q was determined to be 48. Once a phase valuewas measured, Eq. (3) was used to find the resonance frequency and Eq.(2) was used to find the change in mass relative to its value at thelowest RH. Note that the total mass of the cantilever includes the drymass of spores (650 nm thick, 1.5 g/cm³, circular cross section) and thesilicon (1.49 μm thick, 2.33 g/cm³, uniform cross section).

In accordance with one embodiment, the RH can be cycled between 15% and85% at a predefined period, in this example, 5 seconds, and the sporesexpanded and contracted generating a plane stress of 25.2 N/m, as shownin FIG. 2c . During this process, the total mass of the cantileverchanged by 3.5% from the dry state (15% RH) to the hydrated state (85%RH) as shown in FIG. 2d . Considering the density and thickness of thesilicon cantilever, the spore layer absorbed and released ˜0.15 g/m² ofwater. On a flat surface this much water would be expected to create athickness of 150 nm.

As shown in FIG. 2c , the spores respond in ˜0.4 seconds during waterabsorption and ˜0.5 seconds during water release. This relatively fastresponse is useful for energy applications because power levels from aunit area of material directly depend on the rate of evaporation andabsorption and the associated rates of contraction and expansion. Themeasured timescale for drying (˜0.5 sec) and the effective thickness ofwater released in the process (150 nm) correspond to an evaporation rateof ˜300 nm/sec. This is larger than the rate of natural evaporation thatis generally below 2 meters per year (˜63 nm/sec). Interestingly, themeasured rates of water absorption and release by the spores are alsosufficient to respond to the fluctuations in moisture caused byrespiration, which occurs on a time scale of ˜1 sec.

To understand the effect of long term cyclical absorption and release ofwater on the kinetics of shape change, the period of cycles was reducefrom 5 seconds to 2 seconds and the spores were allowed to go throughmore than 1 million cycles over the course of 6 weeks (FIG. 2e ). Thevariations in the strain response reduced only slightly after thisperiod of time (FIG. 2c, f ), highlighting the remarkable reversibilityof the swelling and shrinking process even over many cycles.

Energy Transfer to an External Load

In the above analysis, spores induced a strain of 0.04% and displacedthe free end of the 300 μm long cantilever by 18 μm. While thisrepresents a remarkable actuation capability in the context ofmicromechanical devices, the strain induced and the energy transferredto the substrate can increase significantly with a proper choice ofsubstrate material and thickness. To understand the conditions thatmaximize energy transfer, we used a simple estimate for the maximumstrain in a bilayer plate. For a given ratio of the elastic modulus ofthe passive sheet to the spore layer, there is an optimum ratio ofthicknesses that maximizes the energy transfer, leading to a simpledesign criterion for optimizing these dynamic spore-based hygromorphs asenergy harvesters that correspond to an optimal range of the elasticmodulus and thickness corresponds to millimeter thick rubber sheets.Consequently, we prepared samples by placing spores on natural latexrubber sheets.

FIG. 3a-c shows the changes in the shape of a 0.5 mm thick natural latexrubber sheet induced by a layer of bacterial spores at varying levels ofRH. The sheet is allowed to deform in a horizontal plane to minimize theeffect of gravity. From the observed radii of curvature we determinedthe strain generated by the spores (FIG. 3d ) and the free energyavailable for useful work (FIG. 3e ). At 20% RH, the measured strain of10.9% corresponds to a stress of 23.7 N/m and produces ˜2.6 J/m² freeenergy available for useful work. This corresponds to a work density of˜4 J/cm³ (assuming a thickness of 650 nm for the spore layer), which ishigher than typical work densities achieved by artificial muscles by anorder of magnitude, suggesting the possible use of spores as actuators.The energy density can be even higher. For example, while a similaramount of work can be generated from both spatial directions, cracks inthe spore layer that are largely parallel to the short axis of therubber sheet restricted the transfer of energy to one dimension (FIGS.7A and 7B).

In principle, spores that contracted and equilibrated at low RH can alsogenerate work when they expand in saturated (high RH) air. If twosources of air are available, one saturated and one at low RH, sporescan cyclically absorb water from the saturated air and release it at lowRH, while converting ambient heat into useful work. The maximum workthat can be done in this process is determined by the changes in thefree energy of the water being transferred: w=R_(g)T ln(φ, where w isthe molar work, R_(g) is the gas constant, T is the temperature and ρ isthe RH of air. According to the AFM based measurements of the mass ofthe absorbed water (˜0.15 g/m²), the maximum work that can be done inone cycle is approximately 32 J/m² at 20% RH. Assuming that the energyconverting device based on spores can collect energy from thedisplacements in two directions and equal amounts of work can be done inexpansion and contraction, the spore layer should be able to generate˜10.4 J/m² of work per cycle. This represents an efficiency ofapproximately 30%. The efficiency can be improved by strengthening theadhesion between the neighboring spores, thereby preventing crackformation and increasing the plane stress values. In addition, theexpansion and contraction of spores in the third direction transferswater without generating work. This leakage effect can be mitigated byblocking the expansion of spores in that direction.

In one embodiment, natural latex rubber sheets (Rubber Sheet Roll,Shippensburg, Pa.) were cut into rectangular pieces with scissors. Theirtop surfaces were treated with poly-1-lysine to improve adhesion. Asolution containing B. subtilis spores was placed on pieces of rubbersheet and then allowed to dry in a fume hood. RH of the laboratory airwas approximately 15-20%. The amount of solution to be placed on therubber sheet was determined by visually inspecting spore coverage underan optical microscope. Once the solution dried, the rubber sheetsalready exhibited a curvature because the RH of laboratory air was low(˜15-20%). The sheets were then placed in a chamber with saturated airand kept for a day. This procedure increased the curvature of the rubbersheets once they were placed back to low RH.

The rubber sheet, 0.5 mm thick, was cut into a 2 cm by 6 cm rectangularpiece and coated with a layer of spores. The sheet was attached from thecenter to a piece of acrylic glass with adhesive tape and then placedvertically in a humidity chamber with transparent walls. RH inside thechamber was monitored with a hygrometer (Vaisala). The chamber RH wasgradually increased from the laboratory level (˜18% at the time of themeasurements) by supplying saturated air. Photographs of the latex sheetwere taken from a direction allowing the 2 cm wide edge to be seen.Pictures were taken at intervals of 5% RH starting from 20%.

The plane stress at the spore layer was determined according to theformula:

$\begin{matrix}{\sigma_{x} = {\frac{{Et}^{2}}{6\left( {1 - v^{2}} \right)}\left( {\frac{1}{R_{x}} - {v\frac{1}{R_{y}}}} \right)}} & (4)\end{matrix}$

Here σ_(x) is the surface stress along the direction of the observedcurvature, E is the Young's modulus of the rubber, ν is the Poisson'scoefficient for rubber, t is the thickness of the rubber sheet, andR_(x), R_(y) are the radii of the curvature. t is 0.5 mm for the sheetused in FIG. 3. R_(x) is estimated by fitting the optical pictures ofthe rubber with a circle. R_(y) is assumed to be infinite because therubber sheet exhibited a cylindrical shape. Strain at the surface of therubber sheet near the spores is estimated from 2t/3R_(x) (the neutralplane is 2t/3 below the surface, see also Eqs. 2.3-2.6 of Reyssat, E. &Mahadevan, L., above. We determined E from the stress strain curves fora rectangular strip of the same latex rubber sample (1.3 MPa). ν istaken as 0.5. Note that in contrast to Eq. (1), Eq. (4) accounts foranisotropic stresses in the spore layer. The cylindrical geometry of therubber sheet originated during the spore drying. This shape was stable.Although bifurcations observed in bilayer systems with largedeformations may explain the emergence of a cylindrical shape, weobserved formation of cracks in the spore layer that are largelyparallel to the short axis of the sheet (see FIG. 7B). This suggeststhat stresses, originating along the receding capillary during thesample preparation, were larger than the strength of adhesion betweenthe spores.

Design Principles for Maximum Energy Transfer to an Elastic Substrate

The contracting spore layer exerts a plane stress at the interfacebetween spores and the substrate. As a result, the substrate shapedeforms into a curved surface (FIG. 6). The relationship between theradius of curvature r and plane stress σ is given with the followingformula:

$\begin{matrix}{\sigma = {\frac{E}{6\left( {1 - v} \right)}\frac{t^{2}}{r}}} & (1)\end{matrix}$

Here E is the Young's modulus, ν is the Poisson's coefficient, and t isthe thickness of the elastic substrate. In the resulting curvedgeometry, the strain within the elastic substrate varies linearly withdistance. The neutral plane with zero strain is located 2t/3 away fromthe spore-substrate interface. Therefore, the strain s at the interfaceis given by

$\begin{matrix}{s = \frac{2t}{3r}} & (5)\end{matrix}$

FIG. 6 shows a schematic of an elastic substrate coated with a layer ofbacterial spores deformed by the stress generated by the spores.

Using s, we can rewrite Eq. (1) as follows:

$\begin{matrix}{\sigma = {{\frac{Et}{4\left( {1 - v} \right)}s} = {Ks}}} & (6)\end{matrix}$

Eq. (6) provides the plain stress-strain relationship dictated by theelastic substrate. Strain within the spore layer provides a secondrelationship. Precise modeling of this relationship is complicated bythe complex geometries of spores and their arrangements on the surface.For simplicity, we assume the following linear relationship:

σ=M(s _(dry) −s)  (7)

Here M is the modulus of stretching, s_(dry) is the strain induced inunconstrained spores upon drying, and s is given by Eq. (5). Note thats_(dry) has a negative value and for s_(dry)<s<0, plane stress σ is alsonegative. Equations (6) and (7) can be solved to find equilibrium stressσ₀ and strain s₀ values.

$\begin{matrix}{{\sigma_{0} = {\frac{MK}{M + K}s_{dry}}},\mspace{20mu} {s_{0} = {\frac{M}{M + K}s_{dry}}}} & (8)\end{matrix}$

The energy transferred to the substrate during the drying process can bewritten in terms of the equilibrium stress σ₀ and strain s₀ values asfollows:

$\begin{matrix}{W = {{\int_{s = 0}^{s_{0}}{{\sigma (s)}\ {s}}} = {{\frac{1}{2}\sigma_{0}s_{0}} = {\frac{1}{2}\frac{M^{2}K}{\left( {M + K} \right)^{2}}s_{dry}^{2}}}}} & (9)\end{matrix}$

This equation is maximized when K is equal to M. The modulus ofstretching M is the product of the effective thickness h and theeffective elastic modulus E_(h) of the spore layer. Therefore, thecondition of maximum energy transfer becomes:

$\begin{matrix}{{E_{h}h} = \frac{E_{s}t}{4\left( {1 - v} \right)}} & (10)\end{matrix}$

To estimate the value of the left hand side of Eq. (10), we measuredelastic moduli of the spore coat and the underlying cortex layer withatomic force microscopy and found them to be 13.6 GPa and 6.9 GPa,respectively. To measure the elastic modulus of the cortex, we analyzeda cotE-gerE mutant of B. subtilis, which lacks most of its coat. Thecortex is very likely to be the layer that most readily absorbs waterand swells. Therefore, we approximate E_(h) with 6.9 GPa. The bacterialspore layer has an approximate thickness of 650 nm (typical diameter ofB. subtilis spores). However due to their round shaped cross sections,spores do not make physical contact in the entirety of the 650 nm. Toaccount for this geometrical effect, we assumed h˜300 nm.

According to Eq. (10), for a given substrate material with elasticmodulus E_(s), maximal energy transfer to the substrate takes place atsome specific thickness. In addition, the conditions for maximum energytransfer (K=M) also require s₀ to be s_(dry)/2 (See Eq. (8)). For sporess_(dry) can be as much as 12%. Therefore, materials that cannot sustainlarge strains are not suitable for maximizing energy transfer. In thiswork we used natural latex rubber sheets, which have E_(s)˜1.3 GPa andν˜0.5. Then, according to Eq. (10) the thickness of the rubber sheetshould be 3.15 mm.

Electricity Generation with Spores

To demonstrate the generation of electricity with bacterial spores, weused a commercially available piezoceramic (PZT) transducer. For this,we fixed one edge of a spore-coated rubber sheet and allowed theopposite edge to slide against the surface of the piezoelectric plate(FIG. 4a-c ). The mechanical coupling was limited by the large bendingstiffness of the piezoelectric plate relative to the rubber sheet(>10⁴). Nonetheless, it was possible to generate a potential differenceof 1.4 volts (FIG. 4d ) and deliver approximately 1.4 μJ of electricalenergy in one cycle of high and low RH (FIG. 4e ).

Despite the limited mechanical coupling and frictional losses, theelectrical power generated by the changing relative humidity comparesfavorably against energy harvested from ultrasonic vibrations,suggesting that interfacing with spores may improve the power output ofpiezoelectric nanogenerators. Nevertheless, economically feasiblegeneration of electrical energy requires high efficiencyelectromechanical conversion. A developing technology based ondielectric elastomers shows significant promise for low cost highefficiency electromechanical conversion. These materials are basicallythin sheets of elastomers, such as silicone, coated with compliantelectrodes. When external mechanical forces cyclically stretch andcontract the elastic sheet, the changes in the capacitance between theelectrodes allow converting mechanical energy into electricity.Theoretical work has shown that dielectric elastomers have a capacity togenerate electrical energy of more than 2 Joules per gram of theelastomer in one cycle of stretching and contraction. In principle,spores can be assembled on dielectric elastomers, resulting inpotentially low cost and scalable rubber-based devices.

Electricity can be generated by placing the rubber sheet in contact witha piezoelectric transducer assembly as shown in FIG. 8. Fourpiezoelectric transducers (Piezo Systems, inc. Part no: D220-A4-503YB;0.38 mm thick, 31.4 mm wide, and 62.5 mm long, with Young's modulus ˜50GPa) were attached in a row and the whole assembly was positionedvertically, like an inverted pendulum. In FIG. 8, b is the top mostpiezoelectric transducer and c is the base that holds the stack ofpiezoelectric transducers in position. Additional mass a was placed atthe top with a slider that allowed us to change the height of the massa, and therefore, the effective spring constant. A 0.625 mm thick latexrubber sheet d, 3 cm by 8 cm in size, was coated with a layer of B.subtilis spores. The sheet d was brought into physical contact with thepiezo assembly so that only the 8 cm long edge of the rubber sheet dtouched the piezo material. The opposite edge of the rubber sheet d wasfixed to a Lego™ brick. Moisture was generated by an ultrasonichumidifier (Vicks). See FIGS. 8 and 9. Moist air from the humidifier wasguided through a plastic hose and brought to the vicinity of the rubbersheet. RH surrounding the rubber sheet d was increased or decreased bymoving the open end of the hose close to or away from the sheet d.Voltage generated from the piezoelectric transducers connected in serieswas recorded with a data acquisition card (National Instruments, S-6115)using a 10× oscilloscope probe.

Note that there is large difference in bending stiffness of thepiezoelectric material and the rubber sheet. Consequently, the effectivespring constant of each piezoelectric transducer (˜188 N/m, when fixedat one end) is significantly higher than the effective spring constantof the rubber sheet (˜0.03 N/m, in the flexure mode). The large mismatchin mechanical properties leads to low mechanical coupling. The piezoassembly used here has a lower effective spring constant that improvesenergy transfer from the spore coated rubber sheet.

FIG. 5 shows the areal density of power generation from naturalevaporation under conditions representative of cold, mild and warmweather. Depending on the wind speed, air temperature, relativehumidity, and solar radiation, 1-20 W/m² of power output can beexpected. In FIG. 5, the power extracted from a unit area of evaporatingwater is plotted as a function of surface relative humidity ρ forweather conditions of 200 W/m² net solar radiation, 18° C. airtemperature, and 10 km/h wind speed at 5 values of the RH of air. Powerdensities at optimal ρ values are plotted for cold (blue/bottom; 6° C.,100 W/m²), mild (green/middle; 18° C., 200 W/m²), and warm (orange/top;30° C., 300 W/m²) weather. Calculations are carried out for three windspeeds, 10 km/h (solid line), 20 km/h (dashed line), and 30 km/h (dottedline).

The power density levels in FIG. 5 are comparable to the power densitiesdelivered by existing wind and solar farms, which are around 1-10 W/m².Achieving this power density will require engineering of devices thatfully harness the potential of bacterial spores. If this can beimplemented in platforms like dielectric elastomers, then the cost ofenergy production could be economically feasible.

Both elastomers and bacterial spores are produced in large quantitiesand used in a variety of industries. Bacterial spores also have theimportant advantage that several species (including the one used in thisstudy) are environmentally benign and pose no health risk to humans orother animals. Biological materials with strong hygroscopic properties,such as plant cell walls and spider silk, are potential alternatives tospores in our proposed technology. However, spores are particularlyattractive because of the ease with which they can be produced and builtinto devices, their high work density and durability over a wide rangeof conditions and large numbers of cycles of dehydration.

We have calculated the evaporation rate, surface temperature, and thepower that is extracted from evaporation as a function of the surfacerelative humidity ρ and for a range of the relative humidity of air.Note that p is a variable that can be controlled by the energyconverting devices, which can be tuned to a desired value by adjustingthe load w. FIG. 10a shows evaporation rates calculated for 200 W/m² netsolar radiation, 18° C. air temperature, and 10 km/h wind speed at 5values of RH. As ρ is lowered from unity (w=0), the rate of evaporationgradually declines and the surface temperature rises (FIG. 10b ).Evaporation ultimately vanishes at a certain value of p, at which pointheat is transmitted back to air entirely in the form sensible heat.Importantly, the amount of power extracted from evaporation peaks atcertain values of ρ (FIG. 10c ). For a given weather conditions, theload on the energy converting devices can be adjusted to maximize thepower output. In addition, evaporation rates at optimal values of ρ areapproximately half of the open water evaporation rates (ρ=1) under thesame weather conditions.

Examples

In accordance with one embodiment of the present invention, one or morelayers of bacterial or other spores can be adhered or coupled to thesurface of a piezoelectric material or a piezo polymer, for example asshown in FIG. 2a . The spores can be cyclically exposed to high RH andlow RH air as described above causing the spores to expand and contractand causing the piezoelectric material or piezo polymer to generateelectricity.

The piezo materials can be used in an energy conversion device formedfrom an otherwise unstable structure (this can be a mechanicalinstability like an inverted pendulum, buckling beam, etc). The couplinghelps to bring the overall spring constant of the entire device to nearzero. A near zero spring constant means the system has near zero storedmechanical energy. This will ensure highly efficient electricitygeneration.

In an alternative embodiment, the spores can be embodied in a systemthat periodically exposes the spores to high RH and low RH environmentsas shown in FIGS. 11A and 11B. The system shown in FIGS. 11A and 11Bincludes a plurality bacterial spores 1102 arranged in one or morelayers, encapsulated in an expandable container 1106 that translates theexpansion of the spores 1102 into linear expansion of the container inone or more dimensions. Preferably, the container 1106 is constructedfrom a flexible material and allows for moisture to pass into thecontainer 1106 to be absorbed by the spores 1102 and for moisturereleased by the spores 1102 to pass out of the container 1106. Forexample, the container 1106 can be formed from a flexible mesh material.In addition, the container 1106 can include a bottom shutter mechanism1110 covering the bottom surface and top shutter mechanism 1120 coveringthe top surface of the expandable container. Each shutter mechanism1110, 1120 can include two overlapping plates 1112, 1114, 1122, 1124having a plurality of evenly spaced slots 1116, 1126 such when theplates can move relative each other in a first direction the slots 1116,1126 become either aligned and open or not aligned and closed (blockedby the material between the slots of the other plate). One end of eachplate 1118, 1119, 1128, 1129 of the shutter mechanism can be fastened toor engage opposite ends of the container 1106 such that as the containerexpands the plates of the shutter mechanism move relative to each other.

In operation, the spores 1102 can be dry and contracted in theexpandable container 1106. The bottom shutter mechanism 1110 in thisinitial state is configured such that the slots 1116 are aligned andmoisture from the body of water 1130 below can easily enter thecontainer 1106. In this initial state, the top shutter mechanism 1120can be configured such that the slots 1126 are not aligned and closed,so moisture cannot easily escape the container 1106. From this initialstate, moisture enters the container 1106 from below and the spores 1102begin to swell causing the container 1106 to expand horizontally asindicated by the arrows 1132. As the container 1106 expands the topplate 1122 of the top shutter mechanism 1120 and the bottom plate 1112of the bottom shutter mechanism 1110 move in an opposite direction tothe bottom plate 1124 of the top shutter mechanism 1120 and the topplate 1114 of the bottom shutter mechanism 1110, causing the slots 1116in the bottom shutter mechanism 1110 to close and the slots 1126 in thetop shutter mechanism 1120 to open such that the system reaches theexpanded stated as shown in FIG. 11B. In the expanded state, the topshutter mechanism slots 1126 are open exposing the spores 1102 to a lowRH environment causing the spores 1102 to release moisture and contractcausing the contain 1106 to contract horizontally as indicated by arrows1134 and return to the initial state. Optionally, heat from a heatsource 1140, such as from the Sun or an artificial heat source, can beapplied to increase the release of moisture. The process then repeats.

Naturally occurring evaporation can be powered by the sunlight. Whensome of the light gets reflected from the surface, that power is notused in evaporation. To maximize the use of solar energy forevaporation, the materials in the vicinity of the hygroscopic materialcan be constructed from black colored materials or light absorbingmaterials or nanoparticles.

FIGS. 11C-11E show alternative systems for producing electricity fromthe device shown in FIGS. 11A-11B. In accordance with one embodiment ofthe invention as shown in FIG. 11 C, the linear expanding andcontracting device 1100 of FIGS. 11A-11B can be coupled by one or moretransmission elements or links to a piezo electric device 1150 and theopposite ends of the system can be coupled to fixed anchor points 1136.The system generates electricity by applying expanding and contractingforces on the piezo electric device which converts the mechanical energyto electrical energy.

Similarly, as shown in FIG. 11 D, the linear expanding and contractingdevice 1100 of FIGS. 11A-11B can be coupled by one or more transmissionelements or links to a capacitive device 1150 formed from dielectricelastomer as described below with respect to FIGS. 12C and 12D and theopposite ends of the system can be coupled to fixed anchor points 1136.This system generates electricity by expanding and contracting thedielectric elastomer that serves as the dielectric material between twoplates of a capacitor.

Similarly, as shown in FIG. 11 E, the linear expanding and contractingdevice 1100 of FIGS. 11A-11B can be coupled by one or more transmissionelements or links to an electric generator device 1150 formed from apermanent magnet and one or more coils of wire and one end of the devicecan be coupled to fixed anchor points 1136. This system generateselectricity by applying the expanding and contracting motion to move apermanent magnet relative to a coil of wire to produce electricity.Alternatively, the linear motion can be converted to rotary motion torotate the drive shaft or a rotary generator.

In an alternative embodiment of the invention, the spores according tothe invention can be used to change the distance between plates thatform a capacitor. The spores expand to increase the distance between theplates and decrease the capacitance and then the spores contract todecrease the distance between the plates and increase the capacitance.In an alternate embodiment, the spores contract to increase the distancebetween the plates and decrease the capacitance and then the sporesexpand to decrease the distance between the plates and increase thecapacitance.

Dielectric electroactive polymers (dielectric elastomers) can be used toproduce an electric generator. Dielectric elastomers (DE) are thinrubber dielectric sheets that can be coated with flexible/compliantelectrodes to form a capacitor. Stretching the dielectric elastomerincreases the area of the plates and decreases the space between theplates (and vice versa) to convert mechanical energy into electricity.Their operation is simple and they can run for millions of cycles.

FIGS. 12A and 12B show a hygroscopic material such as bacterial spores1202 attached directly to the DE 1210 and 1212. When DE 1210, 1212 isbiased to a voltage, it can act as an electricity generator. Theexpansion and contraction of the hygroscopic material 1202 will createelectricity. As shown in FIGS. 12A and 12B, the system 1200 looks like aflexible sheet with wires 1222 and 1224 coming from it. The wires 1222and 1224 feed in the electrical bias voltage and take out the generatedelectrical energy. A small battery (such as a thin film battery) canalso be used for initial bias. This flexible sheet can be formed withmultiple layers where the inner layer has the hygroscopic material andthe outer layers control water blockage and transmission.

In an alternative embodiment, the system 1200 can include one or moreports 1230 which can be used to pump humid air and alternately dry airbetween the DE layers to hydrate and dehydrate the hygroscopic material.

FIGS. 12C and 12D show an alternate embodiment of the invention in whicha layer of hygroscopic material, such as bacterial spores 1202, is fixedto a conductive elastic material that serves as the first plate of acapacitor. The capacitor includes a second plate also formed from aconductive elastic material separated by a dielectric elastomermaterial. Optionally, a second layer of hygroscopic material, such asbacterial spores, can be fixed to the second plate. In operation, as thehygroscopic material absorbs moisture and expands causing the plates andthe dielectric elastomer material to expand. Linear expansion of thedielectric elastomer causes it to reduce its thickness resulting in acapacitor with a larger plate area and smaller gap between, increasingthe capacitance of the capacitor. When the device 1200 contracts, theplate area is reduce and the distance between the plates increases,resulting in a decrease in the capacitance of the capacitor. Leads 1222and 1224 can be used to apply a bias potential voltage and allow for thegenerated AC voltage to drawn from the system during expansion andcontraction cycles.

In an alternative embodiment, the device can be constructed from amaterial, such as a sheet material that is adapted to block the passageof water or water vapor on demand. To create cycles of water absorptionand release, the surface that is close to high RH can be configured toblock the water vapor and the hygroscopic material will dry. After apredefined time period, the water blocking can be reversed allowing thehygroscopic material to absorb water vapor and expand.

In a further embodiment, the device can be constructed to allow thehygroscopic material to be exposed to the natural, daily variation inRH. Thus, over the course of a day, the natural variation in RH can besufficient in come locations and environments to cause the expansion andcontraction of device according to the invention.

In an alternative embodiment, the hygroscopic material can be adhered orcoupled to a rotating surface and rotated through a high RH environmentand a low RH environment. When the hygroscopic material is rotated intothe high RH environment, it will absorb water and expand and when thehygroscopic material is rotated into the low RH, it will dry andcontract.

In accordance with one embodiment of the invention, systems containinghygroscopic materials such as bacterial spores can be used to constructenergy storage systems. In accordance with this embodiment an expandablecontainer of spores can be dried and compressed to store energy. As longas the spores in the container are sealed to prevent water and moisturefrom entering the container, the energy can be stored for long periodsof time. To release the energy, a seal can be broken or a port openedallowing moist air or water to be introduced into the container. Thespores will absorb the water and expand causing the container to expand.The container can be coupled to a mechanical device that converts theenergy to electricity or a compressed fluid.

FIGS. 13A and 13B show a system 1300 for storing energy. The system caninclude an expandable container 1306 filled with a plurality of spores1302 (or other hygroscopic material). As shown in FIG. 13A, thecontainer can be compressed as shown by the arrows, packing the sporesin the container 1306. A port 1330 can be provided to on the containerto allow air and moisture to be evacuated from the container as it iscompressed. This will allow the system store energy over a wide range oftemperatures and prevent expansion in cool environments that could causecondensation inside the container 1306. When energy is needed, the port1330 can be opened and water or humid air can be injected into thecontainer causing the spores and the container to expand as shown by thearrows in FIG. 13B. Each container 1306 can be designed to produce apredefined amount of energy and a plurality of containers 1306 can becombined to produce a predefined amount of energy.

FIGS. 14A and 14B show a system 1400 for storing and generating energy.In this embodiment, the hygroscopic material, such as bacterial spores1402, can be fixed to a pre-stressed material, such as plate 1210. Theplate 1210 can be pre-stressed in to the position shown in FIG. 14B andthen biased in to the position shown in FIG. 14A, such as by exposingthe hygroscopic material 1402 to a low RH environment causing thematerial to contract. In this configuration, the device 1400 can act asan energy storage device. In operation, the hygroscopic material 1402can be exposed to water or a high RH environment causing the material toexpand and causing the plate 1210 to move to the position shown in FIG.14B.

In alternative embodiments of the invention, the hygroscopic materialcan be exposed to moisture absorbing (e.g., high RH) and evaporating(e.g., low RH) environments by moving or rotating the device throughthese environments. In still further embodiments, the device can beconfigured to expand and contract based on naturally occurringvariations in environment or a combination of natural and artificialproduced environmental conditions.

In accordance with the invention, the spore (or other hygroscopicmaterials) are available or can be produced in various shapes and sizes.In sheet form, each layer of spores can be arranged in one or morepredefined geometric, pseudo random and random patterns that can beoptimized for energy storage and generation as well as to allow water orhumid air to enable the spores quickly and efficiently be absorbed bythe spores. Further, the spores can be arranged and oriented to producepredictable expansion or contraction along predefined dimensions.

Further, the description refers to bacterial spores, however other typesof spores and hygroscopic materials can be used. As one of ordinaryskill would appreciate, different spores or materials can be selectedbased on their properties and the desired energy release and expansion.

Other embodiments are within the scope and spirit of the invention.

Further, while the description above refers to the invention, thedescription may include more than one invention.

What is claimed is:
 1. A system for generating energy comprising: ahygroscopic material; a generator; a transmission coupled to thehygroscopic material and coupled to the generator to transfer energyfrom the hygroscopic material to the generator; whereby an applicationof a cycle of high relative humidity environment and low relativehumidity environment to the hygroscopic material results in a change insize of the hygroscopic material and energy being transferred to thegenerator.
 2. The system according to claim 1 wherein the hygroscopicmaterial includes microbial spores.
 3. The system according to claim 1wherein the hygroscopic material includes bacterial spores.
 4. Thesystem according to claim 1 wherein the hygroscopic material is adheredto a surface of flexible material layer.
 5. The system according toclaim 1 wherein the hygroscopic material is contained within anexpandable container.
 6. The system according to claim 1 wherein thehygroscopic material is part of a dielectric material in a capacitor. 7.The system according to claim 1 wherein the generator includes a piezoelectric material that produces electricity in response to the change insize of the hygroscopic material.
 8. The system according to claim 1wherein the generator includes an electro-magnetic generator thatproduces electricity in response to the change in size of thehygroscopic material.
 9. The system according to claim 1 wherein heatapplied to the hygroscopic material causes the hygroscopic material tocontract.
 10. The system according to claim 1 wherein a low pressureenvironment applied to the hygroscopic material causes the hygroscopicmaterial to contract.
 11. The system according to claim 1 whereincompression of the hygroscopic material causes the hygroscopic materialto contract.
 12. A method of generating energy comprising: providing ahygroscopic material; providing a transmission coupling the hygroscopicmaterial to a generator; applying a cycle of high relative humidityenvironment and low relative humidity environment to the hygroscopicmaterial results in a change in size of the hygroscopic material,whereby the transmission transfers energy associated with the change insize of the hygroscopic material to the generator and the generatorproduces energy.
 13. The method according to claim 15 wherein thehygroscopic material includes microbial spores.
 14. The method accordingto claim 15 wherein the hygroscopic material includes bacterial spores.15. The method according to claim 15 wherein the hygroscopic material isadhered to a surface of flexible material layer.
 16. The methodaccording to claim 15 wherein the generator includes a piezo electricmaterial that produces electricity in response to the change in size ofthe hygroscopic material.
 17. The method according to claim 15 whereinthe generator includes an electro-magnetic generator that produceselectricity in response to the change in size of the hygroscopicmaterial.
 18. The method according to claim 1 further comprisingapplying heat to the hygroscopic material and causing the hygroscopicmaterial to contract.
 19. The method according to claim 1 furthercomprising applying a low pressure environment to the hygroscopicmaterial and causing the hygroscopic material to contract.
 20. Themethod according to claim 1 further comprising compressing thehygroscopic material and causing the hygroscopic material to contract.